1. Technical Field
The present invention relates to a method of measuring a dimensionless coupling constant of a magnetic structure.
2. Description of Related Art
Magnetization M of a RE-TM (Rare Earth-Transition metal) magnetic structure is composed of two subnetwork magnetizations which are RE magnetization MR and TM magnetization MT. When a RE-dominant case is discussed, a total energy is described In terms of MR and MT, and the subnetwork anisotropy constants KR and KT as follows:Etot=H[MR cos(α−θR)−MT cos(α−θT)]+└KR sin3 θR+KT sin2 θT┘+2π(MR cos θR−MT cos θT)2−λMRMT cos(θR−θT),
wherein H[MR cos(α−θR)−MT cos(α−θT)] is an external energy density; [KR sin3 θR+KT sin2 θT] is an anisotropy energy density; 2π(MR cos θR−MT cos θT)2 is a demagnetizing energy density; and λMRMT cos(θR−θT) is an exchange coupling energy density between RE and TM subnetworks. By calculating the exchange energy between RE and TM atoms per unit volume, the dimensionless coupling constant λ is defined as
      λ    =                  2        ⁢                  (                      Z            +            1                    )                ⁢                                        J                          RE              -              TM                                                                      NG          RE                ⁢                  g          TM                ⁢                  μ          B          2                      ,
wherein Z is an average coordination number (number of nearest neighbor atoms); 2JRE-TM is the exchange energy per RE-TM pair; N is the total atomic number density; gRE and gTM are gyromagnetic factors; and μB (=9.27×10−21 emu) is the Bohr magneton. Therefore, the magnetization reversal intensity can be estimated by the dimensionless coupling constant λ.
Referring to FIG. 1A and FIG. 1B. FIG. 1A is a schematic diagram showing the relationships between the saturation magnetization MS of the magnetic structure and the composition of the magnetic structure, and between the coercivity Hc of the magnetic structure and the composition of the magnetic structure. FIG. 1B is a schematic diagram showing the relationships between the net magnetization MNET of the magnetic structure and the temperature of the magnetic structure, and between the coercivity Hc of the magnetic structure and the temperature of the magnetic structure. In FIG. 1A, the x-axes represents the percentage of the RE atomic content, and the y-axes represents the saturation magnetization MS of the magnetic structure, wherein TM rich represents that the RE atomic content is less than the compensation point content (the compensation point content represents the percentage of the RE atomic content when RE magnetization MR and TM magnetization MT are equal in size and opposite in direction), and RE rich represents that the RE atomic content is more than the compensation point content. The saturation magnetization MS is zero when the compensation point content is reached, the coercivity Hc is maximum; and the dimensionless coupling constant λ is proportional to the coercivity Hc. Therefore, when the RE atomic content is closer to the compensation point content, the greater external magnetic field is needed to reverse the magnetic moments. In FIG. 1B, when the net magnetization MNET is zero, the temperature is a compensation point temperature.
FIG. 2 is a schematic diagram showing the size and direction of to magnetization of the magnetic structure in a RE-dominant case. In FIG. 2, RE magnetization MR and TM magnetization MT are represented by two dimensional (2D) vectors, and M is the sum of the vectors. When the temperature of the magnetic structure is near the compensation point, the magnetizations MR and MT are anti-parallel to make M zero.
θR and θT are very small when the temperature of the magnetic structure is near to the compensation point, so that the Etot equation can be solved by neglecting terms θ2R and θ2T. Moreover, the subnetwork anisotropy fields are defined herein as HR=2KR/MR and HT=2KT/MT, and the solutions of the Etot equation in case of MR>MT can be written as follows:
            θ      R        =                  H        ⁢                                  ⁢        sin        ⁢                                  ⁢                  α          ⁡                      (                                          λ                ⁢                                                                  ⁢                                  M                  s                                            +                              H                T                            -                              H                ⁢                                                                  ⁢                cos                ⁢                                                                  ⁢                α                                      )                                                                                          λ                ⁡                                  (                                                            2                      ⁢                                                                                          ⁢                                              K                        R                                                              +                                          2                      ⁢                                                                                          ⁢                                              K                        T                                                              -                                          4                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                                              M                        s                        2                                                              +                                                                  HM                        s                                            ⁢                      cos                      ⁢                                                                                          ⁢                      α                                                        )                                            +                                                                                          (                                                      H                    T                                    -                                      H                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    α                                    +                                      4                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          M                      s                                                                      )                            ⁢                              (                                                      H                    R                                    +                                      H                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    α                                    -                                      4                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          M                      s                                                                      )                                                                    θ      T        =                  H        ⁢                                  ⁢        sin        ⁢                                  ⁢                  α          ⁡                      (                                          λ                ⁢                                                                  ⁢                                  M                  s                                            -                              H                R                            -                              H                ⁢                                                                  ⁢                cos                ⁢                                                                  ⁢                α                                      )                                                                                          λ                ⁡                                  (                                                            2                      ⁢                                                                                          ⁢                                              K                        R                                                              +                                          2                      ⁢                                                                                          ⁢                                              K                        T                                                              -                                          4                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                                              M                        s                        2                                                              +                                                                  HM                        s                                            ⁢                      cos                      ⁢                                                                                          ⁢                      α                                                        )                                            +                                                                                          (                                                      H                    T                                    -                                      H                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    α                                    +                                      4                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          M                      s                                                                      )                            ⁢                              (                                                      H                    R                                    +                                      H                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    α                                    -                                      4                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          M                      s                                                                      )                                                        
The above solutions includes four unknowns: λ, MR or MT (MS=|MR−MT| can be measured by Alternating Gradient Magnetometer (AGM)), KR and KT. Therefore, it is a complicated problem to find λ experimentally.